Lecture Presentation Chapter 1 Chemistry in Our Lives
What is Chemistry? Chemistry is the study of composition, structure, properties, and reactions of matter. happens all around you every day. Antacid tablets undergo a chemical reaction when dropped in water.
Chemistry and Matter Matter is another word for all substances that make up our world. Matter is defined as anything that has mass and occupies space (volume) Antacid tablets are matter. Water is matter. Glass is matter. Air is matter.
Math Skills Needed For Chemistry
Identifying Place Values For any number, we can identify the place value for each of the digits in that number. The place values for two numbers are listed below: A premature baby has a mass of 2518 grams. A silver coin has a mass of 6.407 grams. Key Math Skill Identifying Place Values
Solving Equations Equations can be rearranged to solve for an unknown variable. 1. Place all like items on one side. 2. Isolate the variable you need to solve for. 3. Check your answer. Key Math Skill Solving Equations
Study Check Solve the following equation for P 1.
Solution Solve the following equation for P 1. To solve for P 1, divide both sides by V 1.
Scientific Notation People have an average of 1 10 5 hairs on the scalp. Each hair is about 8 10 6 m wide. Key Math Skill Writing Numbers in Scientific Notation
1. Scientific Notation Scientists use scientific notation for two reasons: 1. To make it easier to report extremely large or extremely small measurements 2. To report the correct number of significant digits in a measuremed or calculated value We will first focus on reason 1.
1. Scientific Notation Rules for writing a number in scientific notation: Numbers written in scientific notation have two parts: 1. A Coefficient 2. A Power of 10 To write 2400 in the correct scientific notation, Move the decimal place to the left until there is only 1 non zero digit to the left of the decimal place - the coefficient is 2.4. Count the number of places the decimal place was moved that become the coefficient on the the power of 10, which is 3. write the product of the coefficient multiplied by a power of 10. 2.4 10 3
Guide to Converting a Number in Standard Notation Into Scientific Notation Numbers 10 or Greater Step 1: Move the decimal point on the original number to the left until there is only 1 nonzero digit to the left of the decimal place. This becomes the coefficient in scientific notation. Count the number of number places the decimal place was moved to the left. This becomes the positive exponent on the power of 10. Step 2: Write the coefficient multiplied by the power of ten, the exponent on the power of 10 is the number of places you moved the decimal.
Scientific Notation Examples: Numbers 10 or greater 2 400 = 2.4 1 000 = 2.4 10 3 3 places Coefficient Power of 10
Guide to Converting a Number in Standard Notation Into Scientific Notation Numbers less than 1 Step 1: Move the decimal point on the original number to the right until there is only 1 nonzero digit to the left of the decimal place. This becomes the coefficient in scientific notation. Count the number of number places the decimal place was moved to the right. This becomes the negative exponent on the power of 10. Step 2: Write the coefficient multiplied by the power of ten, the exponent on the power of 10 is the number of places you moved the decimal.
Scientific Notation Examples numbers less than 1 0.00086 = = 8.6 10 4 4 places Coefficient Power of 10
Measurements Using Scientific Notation Example: the diameter of chickenpox virus is 0.000 000 3 m = 3 10 7 m
Study Check Write each of the following in correct scientific notation: A. 64 000 B. 0.021
Lecture Presentation Chapter 2 Chemistry and Measurements
2.1 Units of Measurement The metric system is the standard system of measurement used in chemistry. Learning Goal Write the names and abbreviations for the metric or SI units used in measurements of length, volume, mass, temperature, and time.
Units of Measurement Scientists use the metric system of measurement and have adopted a modification of the metric system called the International System of Units as a worldwide standard. The International System of Units (SI) is an official system of measurement used throughout the world for units of length, volume, mass, temperature, and time.
Units of Measurement: Metric and SI
Length: Meter (m), Centimeter (cm) Length in the metric and SI systems is based on the meter, which is slightly longer than a yard. 1 m = 100 cm 1m = 1.09 yd 1 m = 39.4 in. 2.54 cm = 1 in.
Volume: Liter (L), Milliliter (ml) Volume is the space occupied by a substance. The SI unit of volume is m 3 ; however, in the metric system, volume is based on the liter, which is slightly larger than a quart. 1 L = 1000 ml 1 L = 1.06 qt Graduated cylinders are used 946 ml = 1 qt to measure small volumes.
Mass: Gram (g), Kilogram (kg) The mass of an object is a measure of the quantity of material it contains. 1 kg = 1000 g 1 kg = 2.20 lb 454 g = 1 lb The SI unit of mass, the kilogram (kg), is used for larger masses. The metric unit for mass is the gram (g), which is used for smaller masses. On an electronic balance, the digital readout gives the mass of a nickel, which is 5.01 g.
Temperature: Celsius ( C), Kelvin (K) Temperature tells us how hot or cold something is. Temperature is measured using Celsius ( C) in the metric system. Kelvin (K) in the SI system. Water freezes at 32 F, or 0 C. The Kelvin scale for temperature begins at the lowest possible temperature, 0 K. A thermometer is used to measure temperature.
2.2 Measured Numbers and Significant Figures Length is measured by observing the marked lines at the end of a ruler. The last digit in your measurement is an estimate, obtained by visually dividing the space between the marked lines. Learning Goal Identify a number as measured or exact; determine the number of significant figures in a measured number.
Measured Numbers Measured numbers are the numbers obtained when you measure a quantity such as your height, weight, or temperature. To write a measured number, observe the numerical values of the marked lines. estimate the value of the number between the marks. The estimated number is the final number in your measured number.
Measured Numbers for Length The lengths of the objects are measured as A. 4.5 cm. B. 4.55 cm. C. 3.0 cm
Significant Figures In a measured number, the significant figures (SFs) are all the digits, including the estimated digit. Significant figures are used to represent the amount of error associated with a measurement. are all nonzero digits and zeros between digits. are not zeros that act as placeholders before digits. are zeros at the end of a decimal number. Core Chemistry Skill Counting Significant Figures
Measured Numbers: Significant Figures A number is a significant figure (SF) if it is/has
The Atlantic-Pacific Rule For Significant Digits Imagine your number in the middle of the country Pacific Atlantic If a decimal point is present, start counting digits from the Pacific (left) side of the number, The first sig fig is the first nonzero digit, then any digit after that. e.g. 0.003100 would have 4 sig figs 2013 Pearson Education, Inc. Chapter 1, Section 1 31
The Atlantic-Pacific Rule For Significant Digits Imagine your number in the middle of the country Pacific Atlantic If the decimal point is absent, start counting digits from the Atlantic (right) side, starting with the first non-zero digit. The first sig fig is the first nonzero digit, then any digit after that e.g. 31,400 ( 3 sig. figs.) 2013 Pearson Education, Inc. Chapter 1, Section 1 32
Scientific Notation and Significant Zeros When one or more zeros in a large number are significant, they are shown clearly by writing the number in scientific notation. In this book, we place a decimal point after a significant zero at the end of a number. For example, if only the first zero in the measurement 300 m is significant, the measurement is written as 3.0 10 2 m.
Scientific Notation and Significant Zeros Zeros at the end of large standard numbers without a decimal point are not significant. 400 000 g is written with one SF as 4 10 5 g. 850 000 m is written with two SFs as 8.5 10 5 m. Zeros at the beginning of a decimal number are used as placeholders and are not significant. 0.000 4 s is written with one SF as 4 10 4 s. 0.000 0046 g is written with two SFs as 4.6 10 6 g.
Study Check Identify the significant and nonsignificant zeros in each of the following numbers, and write them in the correct scientific notation. A. 0.002 650 m B. 43.026 g C. 1 044 000 L
Solution Identify the significant and nonsignificant zeros in each of the following numbers, and write them in the correct scientific notation. A. 0.002 650 m is written as 2.650 10 3 m. four SFs The zeros preceding the 2 are not significant. The digits 2, 6, 5 are significant. The zero in the last decimal place is significant. B. 43.026 g is written as 4.3026 10 1 g. five SFs The zeros between nonzero digits or at the end of decimal numbers are significant.
Solution Identify the significant zeros and nonsignificant zeros in each of the following numbers, and write them in the correct scientific notation. C. 1 044 000 L is written as 1.044 106 L. four SFs The zeros between nonzero digits are significant. The zeros at end of a number with no decimal point are not significant.
Exact Numbers Exact numbers are not measured and do not have a limited number of significant figures. not used to find the number of significant figures in a calculated answer. numbers obtained by counting. 8 cookies definitions that compare two units. 6 eggs definitions in the same measuring system. 1 qt = 4 cups 1 kg = 1 000 g
Exact Numbers Examples of exact numbers include the following:
Study Check Identify the numbers below as measured or exact, and give the number of significant figures in each measured number. A. 3 coins B. The diameter of a circle is 7.902 cm. C. 60 min = 1 h
2.3 Significant Figures in Calculations A calculator is helpful in working problems and doing calculations faster. Learning Goal Adjust calculated answers to give the correct number of significant figures.
Rules for Rounding Off 1. If the first digit to be dropped is 4 or less, then it and all the following digits are dropped from the number. 2. If the first digit to be dropped is 5 or greater, then the last retained digit of the number is increased by 1. Key Math Skill Rounding Off
Study Check Write the correct value when 3.1457 g is rounded to each of the following: A. three significant figures B. two significant figures
Solution Write the correct value when 3.1457 g is rounded to each of the following: A. To round 3.1457 to three significant figures, drop the final digits, 57. increase the last remaining digit by 1. The answer is 3.15 g. B. To round 3.1457 g to two significant figures, drop the final digits, 457. do not increase the last number by 1, since the first digit dropped is 4. The answer is 3.1 g.
Multiplication and Division: Measured Numbers In multiplication or division, the final answer is written so that it has the same number of significant figures (SFs) as the measurement with the fewest significant figures. Example 1 Multiply the following measured numbers: 24.66 cm 0.35 cm = 8.631 (calculator display) = 8.6 cm 2 (two significant figures) Multiplying four SFs by two SFs gives us an answer with two SFs. Core Chemistry Skill Using Significant Figures in Calculations
Multiplication and Division: Measured Numbers Example 2 Multiply and divide the following measured numbers:
Adding Significant Zeros Adding Zeros: When the calculator display contains fewer SFs than needed, add one or more significant zeros to obtain the correct number of significant figures. Example: Multiply and divide the following measured numbers:
Study Check Perform the following calculation of measured numbers. Give the answer in the correct number of significant figures.
Solution Perform the following calculation of measured numbers. Give the answer in the correct number of significant figures.
Measured Numbers: Addition and Subtraction In addition or subtraction, the final answer is written so that it has the same number of decimal places as the measurement with the fewest decimal places. Example 1 Add the following measured numbers: 2.012 Thousandths place 61.09 Hundredths place + 3.0 Tenths place 66.102 Calculator display 66.1 Answer rounded to the tenths place
Measured Numbers: Addition and Subtraction Example 2 Subtract the following measured numbers: 65.09 Hundredths place 3.0 Tenths place 62.09 Calculator display 62.1 Answer rounded to the tenths place
Study Check Add the following measured numbers: 82.409 mg + 22.0 mg
Solution Add the following measured numbers: 82.409 mg Thousandths place + 22.0 mg Tenths place 104.409 mg Calculator display 104.4 mg Answer rounded to the tenths place
2.4 Prefixes and Equalities Using a retinal camera, an ophthalmologist photographs the retina of the eye. Learning Goal Use the numerical values of prefixes to write a metric equality.
Prefixes A special feature of the SI as well as the metric system is that a prefix can be placed in front of any unit to increase or decrease its size by some factor of ten. For example, the prefixes milli and micro are used to make the smaller units. milligram microgram (mg) (μg or mcg) Core Chemistry Skill Using Prefixes
Metric and SI Prefixes Prefixes That Increase the Size of the Unit
Metric and SI Prefixes Prefixes That Increase Decrease the Size of the Unit
Prefixes and Equalities The relationship of a prefix to a unit can be expressed by replacing the prefix with its numerical value. For example, when the prefix kilo in kilometer is replaced with its value of 1000, we find that a kilometer is equal to 1000 meters. kilometer = 1000 meters (10 3 m) kiloliter = 1000 liters (10 3 L) kilogram = 1000 grams (10 3 g)
Study Check Fill in the blanks with the correct prefix: A. 1000 m = 1 m B. 1 10 3 g = 1 g C. 0.01 m = 1 m
Measuring Length Ophthalmologists measure the diameter of the eye s retina in centimeters (cm), while a surgeon measures the length of a nerve in millimeters (mm). Each of the following equalities describes the same length in a different unit. 1 m = 100 cm = 1 10 2 cm 1 m = 1000 mm = 1 10 3 mm 1 cm = 10 mm = 1 10 1 mm
Measuring Volume Volumes of 1 L or smaller are common in the health sciences. When a liter is divided into 10 equal portions, each portion is called a deciliter (dl). Examples of some volume equalities include the following: 1 L = 10 dl = 1 10 1 dl 1 L = 1000 ml = 1 10 3 ml 1 dl = 100 ml = 1 10 2 ml
Measuring Volume
The Cubic Centimeter The cubic centimeter (abbreviated as cm 3 or cc) is the volume of a cube whose dimensions are 1 cm on each side. A cubic centimeter has the same volume as a milliliter, and the units are often used interchangeably. 1 cm 3 = 1 cc = 1 ml and 1000 cm 3 = 1000 ml = 1 L A plastic intravenous fluid container contains 1000 ml.
The Cubic Centimeter A cube measuring 10 cm on each side has a volume of 1000 cm 3. 10 cm 10 cm 10 cm = 1000 cm 3 = 1000 ml = 1 L
Measuring Mass When you visit the doctor for a physical examination, he or she records your mass in kilograms (kg) and laboratory results in micrograms (μg or mcg). Examples of equalities between different metric units of mass are as follows: 1 kg = 1000 g = 1 10 3 g 1 g = 1000 mg = 1 10 3 mg 1 g = 100 cg = 1 10 2 cg 1 mg = 1000 μg, 1000 mcg = 1 10 3 μg
Study Check Identify the larger unit in each of the following: A. mm or cm B. kilogram or centigram C. ml or μl D. kl or mcl
2.5 Writing Conversion Factors In the United States, the contents of many packaged foods are listed in both U.S. and metric units. Learning Goal Write a conversion factor for two units that describe the same quantity.
Equalities Equalities use two different units to describe the same measured amount. are written for relationships between units of the metric system, U.S. units, or between metric and U.S. units. For example, 1 m = 1000 mm (10 3 mm) 1 lb = 16 oz 2.20 lb = 1 kg Core Chemistry Skill Writing Conversion Factors from Equalities
Equalities: Conversion Factors Any equality can be written as conversion factors. Conversion Factors for the Equality 60 min = 1 h Conversion Factors for the Metric Equality 1 m = 100 cm
Equalities: Conversion Factors and SF The numbers in any equality between two metric units or between two U.S. system units are obtained by definition and are, therefore, exact numbers. As definitions are exact, they are not used to determine significant figures. an equality between metric and U.S. units contains one number obtained by measurement and therefore counts toward the significant figures. Exception: The equality 1 in. = 2.54 cm has been defined as an exact relationship. Therefore, 2.54 is an exact number.
Some Common Equalities
Metric Conversion Factors We can write metric conversion factors. Both are proper conversion factors for the relationship; on is just the inverse of the other.
Metric U.S. System Conversion Factors We can write metric U.S. system conversion factors. In the United States, the contents of many packaged foods are listed in both U.S. and metric units.
Study Check Write conversion factors from the equality for each of the following: A. liters and milliliters B. meters and inches C. meters and kilometers
Solution Write conversion factors from the equality for each of the following: A. B. C.
Equalities and Conversion Factors Within a Problem An equality may also be stated within a problem that applies only to that problem. The car was traveling at a speed of 85 km/h. One tablet contains 500 mg of vitamin C.
Conversion Factors: Dosage Problems Equalities stated within dosage problems for medication can also be written as conversion factors. Keflex (Cephalexin), an antibiotic used for respiratory and ear infections, is available in 250-mg capsules.
Conversion Factors: Percentage, ppm, ppb A percentage (%) is written as a conversion factor by choosing a unit and expressing the numerical relationship of the parts of this unit to 100 parts of the whole. A person might have 18% body fat by mass. To indicate very small ratios, we use parts per million (ppm) and parts per billion (ppb).
Study Check Write the equality and its corresponding conversion factors. Identify each number as exact, or give its significant figures in the following statement: Salmon contains 1.9% omega-3 fatty acids.
Solution Write the equality and its corresponding conversion factors. Identify each number as exact, or give its significant figures in the following statement: Salmon contains 1.9% omega-3 fatty acids. Exact Two SFs
Study Check Write the equality and conversion factor for each of the following: A. Meters and centimeters (length) B. Jewelry that contains 18% gold (percentage) C. One gallon of gas is $3.40.
Solution Write the equality and conversion factor for each of the following: A. Meters and centimeters B. Jewelry that contains 18% gold C. One gallon of gas is $3.40.
2.6 Problem Solving Using Unit Conversion (Also called Dimensional Analysis) Exercising regularly helps reduce body fat. Learning Goal Use conversion factors to change from one unit to another.
Guide to Problem Solving Using Unit Conversion (Dimensional Analysis) The process of problem solving in chemistry often requires one or more conversion factors to change a given unit to the needed unit. Problem solving in chemistry requires identification of the given quantity units. determination of the units needed. identification of conversion factors that connect the given and needed units. Core Chemistry Skill Using Conversion Factors
Guide to Problem Solving Using Unit Conversion Steps for solving problems that contain unit conversions include the following:
Solving Problems Using Unit Conversion Example: If a person weighs 164 lb, what is the body mass in kilograms? STEP 1 State the given and needed quantities. STEP 2 Write a unit plan to convert the given unit to the needed unit. pounds kilograms
Solving Problems Using Unit Conversion Example: If a person weighs 164 lb, what is the body mass in kilograms? STEP 3 State the equalities and conversion factors. STEP 4 Set up the problem to cancel units and calculate the answer.
Study Check A rattlesnake is 2.44-m long. How many centimeters long is the snake?
Solution A rattlesnake is 2.44-m long. How many centimeters long is the snake? STEP 1 State the given and needed quantities. ANALYZE GIVEN NEED THE PROBLEM 2.44 m centimeters STEP 2 Write a unit plan to convert the given unit to the needed unit. meters Metric Factor centimeters
Solution A rattlesnake is 2.44-m long. How many centimeters long is the snake? STEP 3 State the equalities and conversion factors. STEP 4 Set up the problem to cancel units and calculate the answer.
Using Two or More Conversion Factors In problem solving, two or more conversion factors are often needed to complete the change of units. in setting up these problems, one factor follows the other. each factor is arranged to cancel the preceding unit until the needed unit is obtained.
Using Two or More Conversion Factors Example: A doctor s order prescribed a dosage of 0.150 mg of Synthroid. If tablets contain 75 mcg of Synthroid, how many tablets are required to provide the prescribed medication? STEP 1 State the given and needed quantities. ANALYZE GIVEN NEED THE PROBLEM 0.150 mg Synthroid number of tablets STEP 2 Write a plan to convert the given unit to the needed unit. milligrams Metric Factor micrograms Clinical Factor number of tablets
Using Two or More Conversion Factors Example: A doctor s order prescribed a dosage of 0.150 mg of Synthroid. If tablets contain 75 mcg (75 µg) of Synthroid, how many tablets are required to provide the prescribed medication? STEP 3 State the equalities and conversion factors. STEP 4 Set up the problem to cancel units and calculate the answer.
Study Check How many minutes are in 1.4 days?
Solution How many minutes are in 1.4 days? STEP 1 State the given and needed quantities. ANALYZE GIVEN NEED THE PROBLEM 1.4 days minutes STEP 2 Write a plan to convert the given unit to the needed unit. Time Factor Time Factor days hours minutes
Solution How many minutes are in 1.4 days? STEP 3 State the equalities and conversion factors. STEP 4 Set up the problem to cancel units and calculate the answer.
Study Check A red blood cell has a diameter of approximately 10 µm. What is the diameter of the red blood cell in cm?
Solution A red blood cell has a diameter of approximately 10 µm. What is the diameter of the red blood cell in cm? STEP 1 State the given and needed quantities. ANALYZE GIVEN NEED THE PROBLEM 10 µm cm STEP 2 Write a unit plan to convert the given unit to the needed unit. Metric Factor Metric factor micrometers meters centimeters
Solution A red blood cell has a diameter of approximately 10 µm. What is the diameter of the red blood cell in cm? STEP 3 State the equalities and conversion factors. 1 µm = 10-6 m 1 cm = 10-2 m 1 µm or 10-6 m 1 cm or 10-2 m 10-6 m 1 µm 10-2 m 1 cm STEP 4 Set up the problem to cancel units and calculate the answer. 10 µm x 10-6 m x 1 cm = 1 x 10-3 cm 1µm 10-2 m
Study Check If your pace on a treadmill is 65 meters per minute, how many minutes will it take for you to walk a distance of 7.5 kilometers?
Solution If your pace on a treadmill is 65 meters per minute, how many minutes will it take for you to walk a distance of 7.5 kilometers? STEP 1 State the given and needed quantities. ANALYZE GIVEN NEED THE PROBLEM 65 meters/min minutes 7.5 kilometers STEP 2 Write a plan to convert the given unit to the needed unit. Metric Factor Speed Factor kilometers meters minutes
Solution If your pace on a treadmill is 65 meters per minute, how many minutes will it take for you to walk a distance of 7.5 kilometers? STEP 3 State the equalities and conversion factors. STEP 4 Set up the problem to cancel units and calculate the answer.
2.7 Density Learning Goal Calculate the density of a substance; use the density to calculate the mass or volume of a substance. Objects that sink in water are more dense than water; objects that float are less dense.
Densities of Common Substances
Calculating Density Density compares the mass of an object to its volume.
Density of Solids The density of a solid can be determined by dividing the mass of an object by its volume.
Density Using Volume Displacement The density of the solid zinc object is calculated by dividing its mass by its displaced volume. To determine its displaced volume, submerge the solid in water so that it displaces water that is equal to its own volume. Density calculation: 45.0 ml 35.5 ml = 9.5 ml = 9.5 cm 3
Study Check What is the density (g/cm 3 ) of a 48.0 g sample of a metal if the level of water in a graduated cylinder rises from 25.0 ml to 33.0 ml after the metal is added? 25.0 ml 33.0 ml object
Solution What is the density (g/cm 3 ) of a 48.0 g sample of a metal if the level of water in a graduated cylinder rises from 25.0 ml to 33.0 ml after the metal is added?
Problem Solving Using Density If the volume and the density of a sample are known, the mass in grams of the sample can be calculated by using density as a conversion factor. Core Chemistry Skill Using Density as a Conversion Factor
Problem Solving Using Density Example: John took 2.0 teaspoons (tsp) of cough syrup. If the syrup had a density of 1.20 g/ml and there is 5.0 ml in 1 tsp, what was the mass, in grams, of the cough syrup? STEP 1 State the given and needed quantities. ANALYZE GIVEN NEED THE PROBLEM 2.0 tsp syrup density of syrup (1.20 g/ml) grams of syrup STEP 2 Write a plan to calculate the needed quantity. U.S. Metric Factor Density Factor teaspoons milliliters grams
Problem Solving Using Density John took 2.0 teaspoons (tsp) of cough syrup. If the syrup had a density of 1.20 g/ml and there is 5.0 ml in 1 tsp, what was the mass, in grams, of the cough syrup? STEP 3 Write the equalities and their conversion factors, including density.
Problem Solving Using Density John took 2.0 teaspoons (tsp) of cough syrup. If the syrup had a density of 1.20 g/ml and there is 5.0 ml in 1 tsp, what was the mass, in grams, of the cough syrup? STEP 4 Set up the problem to calculate the needed quantity.
Specific Gravity Specific gravity (sp gr) is a relationship between the density of a substance and the density of water. is calculated by dividing the density of a sample by the density of water, which is 1.00 g/ml at 4 C. is a unitless quantity. A substance with a specific gravity of 1.00 has the same numerical value as the density of water (1.00 g/ml).
Study Check An unknown liquid has a density of 1.32 g/ml. What is the volume (ml) of a 14.7-g sample of the liquid?
Specific Gravity Specific gravity (sp gr) is a relationship between the density of a substance and the density of water. is calculated by dividing the density of a sample by the density of water, which is 1.00 g/ml at 4 C. is a unitless quantity. A substance with a specific gravity of 1.00 has the same numerical value as the density of water (1.00 g/ml).